{{Short description|Indian mathematician and astronomer (1444–1544)}} {{More citations needed|date=April 2024}} {{Use dmy dates|date=August 2019 | cs1-dates=sy}} {{Use Indian English|date=August 2019}} {{infobox person | name = Nilakantha Somayaji | caption = | birth_name = | birth_date = 14 June 1444 | birth_place = [[Tirur]], [[Kingdom of Tanur]] | death_date = 1544{{citation needed|date=February 2020}} | death_place = | resting_place_coordinates = | citizenship = | other_names = Kelallur Comatiri | known_for = Authorship of [[Tantrasamgraha]] | education = | alma_mater = | employer = | notable_works = Golasara, Candrachayaganita, Aryabhatiya-bhashya, [[Tantrasamgraha]] | occupation = Astronomer-mathematician | years_active = | title = Somayaji | boards = | spouse = Arya | partner = | children = Rama, Dakshinamurti | parents = Jatavedan (father) | relatives = }} '''Keļallur Nīlakaṇṭha Somayāji''' (14 June 1444 – 1544), also referred to as '''Keļallur Comatiri''',{{cite journal|last=K.D. Swaminathan|date=1972|title=Jyotisa in Kerala|journal=Indian Journal of History of Science|volume=8|issue=1 & 2|pages=28–36|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b62_28.pdf|access-date=3 February 2010}} was a [[Indian mathematics|mathematician]] and [[Indian astronomy|astronomer]] of the [[Kerala school of astronomy and mathematics]]. One of his most influential works was the comprehensive astronomical treatise ''[[Tantrasamgraha]]'' completed in 1501. He had also composed an elaborate commentary on [[Aryabhatiya]] called the ''Aryabhatiya Bhasya''. In this Bhasya, Nilakantha had discussed [[infinite series]] expansions of [[trigonometric functions]] and problems of [[algebra]] and [[spherical geometry]]. ''Grahapariksakrama'' is a manual on making observations in astronomy based on instruments of the time. ==Early life== Nilakantha was born into a [[Malayali Brahmin|Brahmin]] family which came from [[South Malabar]] in [[Kerala]].{{Cite web|title=Nilakantha - Biography|url=https://mathshistory.st-andrews.ac.uk/Biographies/Nilakantha/|access-date=2022-01-11|website=Maths History|language=en}} ==Biographical details== Nilakantha Somayaji was one of the very few authors of the scholarly traditions of India who had cared to record details about his own life and times.{{cite web|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_s1.pdf|title=Tantrasamgraha with English translation|editor=[[K.V. Sarma]]|others=Translated by V.S. Narasimhan|publisher=Indian National Academy of Science|pages=48|language=sa, en|access-date=17 January 2010|url-status=dead|archive-url=https://web.archive.org/web/20120309014402/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_s1.pdf|archive-date=9 March 2012}}''Tantrasamgraha'', ed. [[K.V. Sarma]], trans. V. S. Narasimhan in the Indian Journal of History of Science, issue starting Vol. 33, No. 1 of March 1998 In one of his works titled ''[[Siddhanta]]-star'' and also in his own commentary on ''Siddhanta-darpana'', Nilakantha Somayaji stated that he was born on [[Kali Yuga|Kali-day]] 1,660,181 which works out to 14 June 1444 CE. A contemporary reference to Nilakantha Somayaji in a [[Malayalam]] work on [[astrology]] implies that Somayaji lived to a ripe old age even to become a centenarian. [[Sankara Variar]], a pupil of Nilakantha Somayaji, in his commentary on [[Tantrasamgraha]] titled ''Tantrasamgraha-vyakhya'', points out that the first and last verses of [[Tantrasamgraha]] contain chronograms specifying the Kali-days of the commencement (1,680,548) and of completion (1,680,553) of Somayaji's magnum opus [[Tantrasamgraha]]. Both these days occur in 1500 CE. In [[Aryabhatiya]]-bhashya, Nilakantha Somayaji has stated that he was the son of Jatavedas and he had a brother named '''Sankara'''.{{cite book |last1=K. V. Sarma |title=A History of the Kerala School of Hindu Astronomy |date=1972 |publisher=Vishveshvaranand Institute of Sanskrit and Indological Studies, Panjab University, Hoshiarpur |url=https://archive.org/details/KeralaSchoolOfAstronomy/page/n71/mode/2up?view=theater|access-date=15 July 2024| page=58}} Somayaji has further stated that he was a Bhatta belonging to the Gargya [[gotra]] and was a follower of [[Shakha|Asvalayana-sutra]] of [[Rigveda]]. References in his own ''Laghuramayana'' indicate that Nilakantha Somayaji was a member of the Kelallur family (Sanskritised as Kerala-sad-grama) residing at Kundagrama, now known as [[Thrikkandiyoor|Trikkandiyur]] in modern [[Tirur]], [[Kerala]]. His wife was named Arya and he had two sons Rama and Dakshinamurti. Nilakantha Somayaji studied [[vedanta]] and some aspects of astronomy under one Ravi. However, it was [[Damodara]], son of Kerala-drgganita author [[Paramesvara]], who initiated him into the science of astronomy and instructed him in the basic principles of mathematical computations. The great [[Malayalam]] poet [[Thunchaththu Ramanujan Ezhuthachan]] is said to have been a student of Nilakantha Somayaji. The epithet ''Somayaji'' is a title assigned to or assumed by a [[Namputiri]] who has performed the vedic ritual of ''[[Somayajna]]''.{{cite web|url=http://www.namboothiri.com/articles/yajnam.htm|title=Yaagam (Yajnam)|last=P. Vinod Bhattathiripad|author2=K.D. Nambudripad |date=3 May 2007|publisher=Namboothiri Websites Trust|access-date=4 February 2010}} So it could be surmised that Nilakantha Somayaji had also performed a ''Somayajna'' ritual and assumed the title of a ''Somayaji'' in later life. In colloquial Malayalam usage the word Somayaji has been corrupted to Comatiri. Somayāji’s "Āryabhaṭīyabhāṣya" is the most extensive commentary on Āryabhaṭīya. He takes all pains to expose the rationale and the objective behind the statements and observations made by Āryabhaṭa.''Nilakantha's critique on Aryabhata's verses on squaring and square rooting'', N. K. Sundareswaran, ''[https://www.printspublications.com/journal/gb Ganita Bharati]'', Vol 39, No. 2, 2017 ==Nilakantha Somayaji as a polymath == Nilakantha's writings substantiate his knowledge of several branches of Indian philosophy and culture. It is said that he could refer to a Mimamsa authority to establish his view-point in a debate and with equal felicity apply a grammatical dictum to the same purpose. In his writings he refers to a Mimamsa authority, quotes extensively from Pingala's chandas-sutra, scriptures, Dharmasastras, Bhagavata and Vishnupurana also. Sundararaja, a contemporary Tamil astronomer, refers to Nilakantha as sad-darshani-parangata, one who had mastered the six systems of Indian philosophy. ==Astronomy== In his ''[[Tantrasangraha]]'', Nilakantha revised [[Aryabhata]]'s model for the planets [[Mercury (planet)|Mercury]] and [[Venus]]. According to [[George Gheverghese Joseph|George G. Joseph]] his equation of the [[Center of mass|centre]] for these planets remained the most accurate until the time of [[Johannes Kepler]] in the 17th century.George G. Joseph (2000). ''The Crest of the Peacock: Non-European Roots of Mathematics'', p. 408. [[Princeton University Press]]. In his ''Aryabhatiyabhasya'', a commentary on Aryabhata's ''[[Aryabhatiya]]'', Nilakantha developed a computational system for a partially [[heliocentrism|heliocentric]] planetary model in which Mercury, Venus, [[Mars]], [[Jupiter]] and [[Saturn]] orbit the [[Sun]], which in turn orbits the [[Earth]], similar to the [[Tychonic system]] later proposed by [[Tycho Brahe]] in the late 16th century. Most astronomers of the Kerala school who followed him accepted this planetary model.K. Ramasubramanian, M. D. Srinivas, M. S. Sriram (1994). "[https://physics.iitm.ac.in/~labs/amp/kerala-astronomy.pdf Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 AD) and the implied heliocentric picture of planetary motion]", ''[[Current Science]]'' '''66''', p. 784-790. Somayaji time and again advocates the necessity of periodical modification of computation system based on observations and experimentations. One of his works, ''Jyotirmimamsa'', is written exclusively for this purpose. His critical and analytical approach is reflected in all works.{{cite book |title=Kerala School of Mathematics:Trajectories and Impact |date=2014 |publisher=University of Calicut |isbn=9788193116807 |edition=2014 |ref=The critical and rational approach of Kelallur Nilakantha Somayaji}} ==Works == {{further|Tantrasamgraha|Jyotirmimamsa}} The following is a brief description of the works by Nilakantha Somayaji dealing with astronomy and mathematics.{{cite journal|last=A.K. Bag|date=1980|title=Indian literature on mathematics during 1400 - 1800 AD|journal=Indian Journal of History of Science|volume=15|issue=1|pages=79–93|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005af2_79.pdf|access-date=30 January 2010|url-status=dead|archive-url=https://web.archive.org/web/20120309124530/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005af2_79.pdf|archive-date=9 March 2012}} #''[[Tantrasamgraha]]'' #''Golasara'' : Description of basic astronomical elements and procedures #''Sidhhantadarpana'' : A short work in 32 slokas enunciating the astronomical constants with reference to the Kalpa and specifying his views on astronomical concepts and topics. #''Candrachayaganita'' : A work in 32 verses on the methods for the calculation of time from the measurement of the shadow of the [[gnomon]] cast by the moon and vice versa. #''Aryabhatiya-bhashya'' : Elaborate commentary on Aryabhatiya. #''Sidhhantadarpana-vyakhya'' : Commentary on his own Siddhantadarapana. #''Chandrachhayaganita-vyakhya'' : Commentary on his own Chandrachhayaganita. #''Sundaraja-prasnottara'' : Nilakantha's answers to questions posed by Sundaraja, a Tamil Nadu-based astronomer. #''Grahanadi-grantha'' : Rationale of the necessity of correcting old astronomical constants by observations. #''Grahapariksakrama'' : Description of the principles and methods for verifying astronomical computations by regular observations. #''[[Jyotirmimamsa]]'' : Analysis of astronomy ==See also== *[[Indian mathematicians]] *[[Indian astronomy]] *[[List of astronomers and mathematicians of the Kerala school]] ==References== {{reflist}} ==Further reading== *{{cite book |last=N. K. Sundareswaran |title=The Contribution of Kelallur Nilakantha Somayaji to Astronomy |publisher=University of Calicut |year=2009 |isbn=9788177481495 |edition=2009 |location=Calicut |language=English}} *{{cite journal|last=R.C. Gupta|title=Second order interpolation in Indian mathematics up to the fifteenth century|journal=Indian Journal of History of Science|volume=4|issue=1 & 2|pages=87–98|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b65_86.pdf|url-status=dead|archive-url=https://web.archive.org/web/20120309121926/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b65_86.pdf|archive-date=2012-03-09}} * [[K. V. Sarma]] (2008) "Nilakantha Somayaji", [[Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures]] (2nd edition) edited by [[Helaine Selin]], Springer, {{ISBN|978-1-4020-4559-2}}. *{{cite journal|last=Shailesh A Shirali|date=May 1997|title=Nilakantha, Euler and pi|journal=Resonance|pages=28–43|url=http://www.ias.ac.in/article/fulltext/reso/002/05/0029-0043|access-date=6 September 2016}} *{{cite journal|last=Ranjan Roy|date=Dec 1990|title=The discovery of the series formula for π by Leibnitz, Gregory and Nilakantha|journal=Mathematics Magazine|volume=63|issue=5|pages=291–306|url=http://www.maa.org/programs/maa-awards/writing-awards/carl-b-allendoerfer-awards/the-discovery-of-the-series-formula-for-pi|access-date=6 September 2016|doi=10.1080/0025570X.1990.11977541 |jstor=2690896 |archive-url=https://web.archive.org/web/20170402174836/https://maa.org/programs/maa-awards/writing-awards/carl-b-allendoerfer-awards/the-discovery-of-the-series-formula-for-pi |url-status=dead |archive-date=2017-04-02}} ==External links== {{commons category|Nilakantha Somayaji}} * [https://chenthala.in/ Official Website of Chenthala Vishnu Temple] {{Webarchive|url=https://web.archive.org/web/20210419040300/https://chenthala.in/ |date=2021-04-19 }} * [https://chenthala.in/tantrasamgraham-tantra-sangraha-of-somayaji/ Tantrasamgraha Official Website] {{Webarchive|url=https://web.archive.org/web/20210510155139/https://chenthala.in/tantrasamgraham-tantra-sangraha-of-somayaji/ |date=2021-05-10 }} * [https://web.archive.org/web/20210623220251/https://chenthala.in/kelallur-nilakantha-somayajipadu/ Official Website of Kelallur Nilakantha Somayaji] (archived) {{Kerala School}} {{Indian mathematics}} {{Authority control}} {{DEFAULTSORT:Somayaji, Nilakantha}} [[Category:1444 births]] [[Category:1544 deaths]] [[Category:Indian Hindus]] [[Category:16th-century Indian astronomers]] [[Category:Scientists of the Kerala school of astronomy and mathematics]] [[Category:15th-century Indian mathematicians]] [[Category:16th-century Indian mathematicians]] [[Category:People from Malappuram district]] [[Category:15th-century Indian astronomers]]